There have also been several other works on developing optimal scheduling policy for minimizing AoI for EH sensor networks [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. For example, [1]} has investigated optimal online policy for single sensor single sink system with a noiseless channel for infinite, finite and unit size battery capacity; for finite battery size, it has provided energy aware status update policy. The paper
[2]} has considered a multi-sensor single sink system with infinite battery size, and proposed a randomized myopic scheduling scheme. For an EH source with finite battery and Poisson energy arrival process, the authors in [3]} have provided age-energy trade-off and optimal threshold policy for AoI minimization, but unlike our work, they do not consider probing/estimation of a fading channel while making a sampling decision.
In [4]}, the optimal online status update policy to minimize the long run average AoI for EH source with updating erasures have been proposed. It has been shown that the best effort uniform updating policy is optimal when there is no feedback and best-effort uniform updating with re-transmission (BUR) policy is optimal when feedback is available to the source. The authors of
[5]} examined the problem of minimizing AoI under a constraint on the count of status updates. The authors of [6]} addressed AoI minimization problem for cognitive radio communication system with EH capability; they formulated optimal sensing and updating for perfect and imperfect sensing as a partially observable Markov decision process (POMDP). Information source diversity, i.e., multiple sources tracking the same process but with dissimilar energy cost, and sending status updates to the EH monitoring node with finite battery size, has been considered in [7]} with an MDP formulation, but no structure was provided for the optimal policy. In [8]}, reinforcement learning has been used to minimize AoI for a single EH sensor with HARQ protocol, but no clear intuition on the policy structure was provided. In [10]}, the authors have formulated optimal transmission schemes for an EH sensor which sends update packets to the BS by considering different transmission modes (controlled by power and error probability) and battery recovery setting as an MDP. The authors of [11]} have developed a threshold policy for minimizing AoI for a single sensor single sink system with erasure channel and no channel feedback. For a system with Poisson energy arrival, unit battery size and error-free channel, it has shown that a threshold policy achieves average age lower than that of zero-wait policy; based on this, lower bound on average age for general battery size and erasure channel has been derived. The papers [22]} and [23]} have proposed threshold based sampling policies for AoI minimization in a multi-source system, and also use deep reinforcement learning to learn the optimal policy. However, these paper do not consider channel probing as done in our paper. A very similar claim applies to [24]} which also proposes threshold-based scheduling policy.
